presents the same side to the earth; the other declared that the moon does not revolve on its own axis, for the same reason. Both conclusions were perfectly correct, according to the point of view from which the motions of the moon were considered.50 The antinomies stand in the order of the four transcendental ideas above detailed.
51 We may consider an undetermined quantity as a whole, when it is enclosed within limits, although we cannot construct or ascertain its totality by measurement, that is, by the successive synthesis of its parts. For its limits of themselves determine its completeness as a whole.
52 Space is merely the form of external intuition (formal intuition), and not a real object which can be externally perceived. Space, prior to all things which determine it (fill or limit it), or, rather, which present an empirical intuition conformable to it, is, under the title of absolute space, nothing but the mere possibility of external phenomena, in so far as they either exist in themselves, or can annex themselves to given intuitions. Empirical intuition is therefore not a composition of phenomena and space (of perception and empty intuition). The one is not the correlate of the other in a synthesis, but they are vitally connected in the same empirical intuition, as matter and form. If we wish to set one of these two apart from the other — space from phenomena — there arise all sorts of empty determinations of external intuition, which are very far from being possible perceptions. For example, motion or rest of the world in an infinite empty space, or a determination of the mutual relation of both, cannot possibly be perceived, and is therefore merely the predicate of a notional entity.
53 The quantum in this sense contains a congeries of given units, which is greater than any number — and this is the mathematical conception of the infinite.
54 It is evident that what is meant here is, that empty space, in so far as it is limited by phenomena — space, that is, within the world — does not at least contradict transcendental principles, and may therefore, as regards them, be admitted, although its possibility cannot on that account be affirmed.
55 Objectively, time, as the formal condition of the possibility of change, precedes all changes; but subjectively, and in consciousness, the representation of time, like every other, is given solely by occasion of perception.
56 The word begin is taken in two senses. The first is active — the cause being regarded as beginning a series of conditions as its effect (infit). The second is passive — the causality in the cause itself beginning to operate (fit). I reason here from the first to the second.
Section III. Of the Interest of Reason in these Self-contradictions.
We have thus completely before us the dialectical procedure of the cosmological ideas. No possible experience can present us with an object adequate to them in extent. Nay, more, reason itself cannot cogitate them as according with the general laws of experience. And yet they are not arbitrary fictions of thought. On the contrary, reason, in its uninterrupted progress in the empirical synthesis, is necessarily conducted to them, when it endeavours to free from all conditions and to comprehend in its unconditioned totality that which can only be determined conditionally in accordance with the laws of experience. These dialectical propositions are so many attempts to solve four natural and unavoidable problems of reason. There are neither more, nor can there be less, than this number, because there are no other series of synthetical hypotheses, limiting a priori the empirical synthesis.
The brilliant claims of reason striving to extend its dominion beyond the limits of experience, have been represented above only in dry formulae, which contain merely the grounds of its pretensions. They have, besides, in conformity with the character of a transcendental philosophy, been freed from every empirical element; although the full splendour of the promises they hold out, and the anticipations they excite, manifests itself only when in connection with empirical cognitions. In the application of them, however, and in the advancing enlargement of the employment of reason, while struggling to rise from the region of experience and to soar to those sublime ideas, philosophy discovers a value and a dignity, which, if it could but make good its assertions, would raise it far above all other departments of human knowledge — professing, as it does, to present a sure foundation for our highest hopes and the ultimate aims of all the exertions of reason. The questions: whether the world has a beginning and a limit to its extension in space; whether there exists anywhere, or perhaps, in my own thinking Self, an indivisible and indestructible unity — or whether nothing but what is divisible and transitory exists; whether I am a free agent, or, like other beings, am bound in the chains of nature and fate; whether, finally, there is a supreme cause of the world, or all our thought and speculation must end with nature and the order of external things — are questions for the solution of which the mathematician would willingly exchange his whole science; for in it there is no satisfaction for the highest aspirations and most ardent desires of humanity. Nay, it may even be said that the true value of mathematics — that pride of human reason — consists in this: that she guides reason to the knowledge of nature — in her greater as well as in her less manifestations — in her beautiful order and regularity — guides her, moreover, to an insight into the wonderful unity of the moving forces in the operations of nature, far beyond the expectations of a philosophy building only on experience; and that she thus encourages philosophy to extend the province of reason beyond all experience, and at the same time provides it with the most excellent materials for supporting its investigations, in so far as their nature admits, by adequate and accordant intuitions.
Unfortunately for speculation — but perhaps fortunately for the practical interests of humanity — reason, in the midst of her highest anticipations, finds herself hemmed in by a press of opposite and contradictory conclusions, from which neither her honour nor her safety will permit her to draw back. Nor can she regard these conflicting trains of reasoning with indifference as mere passages at arms, still less can she command peace; for in the subject of the conflict she has a deep interest. There is no other course left open to her than to reflect with herself upon the origin of this disunion in reason — whether it may not arise from a mere misunderstanding. After such an inquiry, arrogant claims would have to be given up on both sides; but the sovereignty of reason over understanding and sense would be based upon a sure foundation.
We shall at present defer this radical inquiry and, in the meantime, consider for a little what side in the controversy we should most willingly take, if we were obliged to become partisans at all. As, in this case, we leave out of sight altogether the logical criterion of truth, and merely consult our own interest in reference to the question, these considerations, although inadequate to settle the question of right in either party, will enable us to comprehend how those who have taken part in the struggle, adopt the one view rather than the other — no special insight into the subject, however, having influenced their choice. They will, at the same time, explain to us many other things by the way — for example, the fiery zeal on the one side and the cold maintenance of their cause on the other; why the one party has met with the warmest approbations, and the other has always been repulsed by irreconcilable prejudices.
There is one thing, however, that determines the proper point of view, from which alone this preliminary inquiry can be instituted and carried on with the proper completeness — and that is the comparison of the principles from
